Causality is the principal that there is a relationship between a cause and an effect or outcome. In some situations, an outcome may have been the result of one of many causes. Various models and theories exists that try to formalize causal relationships. One such set of models is referred to as the independence of causal influences (ICI), which addresses the issue of exponential growth of parameters when dealing with conditional probabilities by making the assumption of independence of causal influences (ICI). Accepting this assumption allows for parametric models that define conditional probability distributions using only a number of parameters that is linear in the number of causes.
ICI models, such as the Noisy-OR and the Noisy-AND gates, have been widely used. Noisy-OR model is a causal independence formalism that models relationship between a number of causes and an outcome, where each cause is sufficient for resulting in the outcome. The “noisy” modifier emphasizes that any causal relationship is, above all, probabilistic. Noisy-AND model is a causal independence formalism that models relationship between a number of causes and an outcome, where each cause is necessary for resulting in the outcome.
Noisy-OR maybe illustrated using equation Pr(o)=1−[(1−leak) Π(1−pi)], where pi is the probability of cause i causing outcome o; and leak is the probability of observing outcome o without any causes causing it. Noisy-AND maybe illustrated using equation Pr(o)=(1−inhibit) Π(1−pi), where pi is the probability of cause i causing outcome o; and inhibit is the probability of not observing outcome o with all the required causes.
In real life, many Noisy-OR events may overlap. The sufficient causes for outcome A may overlap with those for outcome B. For example, in Quick Medical Reference-Decision Theoretic (QMR-DT), which is a medical decision-support system that is based on the comprehensive Quick Medical Reference (QMR) knowledge base, pneumonia and flu are both sufficient causes for the observable outcome fever. If a patient describes a fever symptom, the question then becomes, “How do medical practitioners determine if the patient has pneumonia or flu or something else?” Or, in a different context, using an alarm system as an example, a wandering stray cat and an actual break-in burglary are both sufficient conditions to trigger the alarm; therefore, a question may be asked, “How does one determine whether this is a false alarm?”
Therefore, there is a need for systems and methods to infer the most probable cause from one or more observable outcomes and causal relations.